系泊海洋平台周期运动倍周期分岔的胞映射分析

Investigation to the Periodic Motions and Period-Doubling Bifurcations of a Moored Ocean Platform with Cell-to-Cell Mapping Method

应用胞映射方法研究了系泊海洋生产平台的周期运动及其倍周期分岔。系泊运动的数学模型是一个具有指数回复力特性的非线性强迫振子 ,以波浪作用力为外激励。将波浪激励周期作为分岔控制参数 ,研究了周期系泊运动的倍周期分岔。胞映射方法用于寻找系统的稳定吸引子并确定其吸引域。时间历程、相图、功率谱和Poincar啨映射用于确定吸引子的具体类型芯糠⑾?,分岔参数处于不同的区域时 ,系统存在着相异的倍周期分岔特性。观察到了倍周期分岔的产生和突然消失 ,也找到了一个趋于吸引子的倍周期分岔序列。根据吸引域的胞映射分析结果解释了上述不同的倍周期分岔特征。发现其原因在于倍周期序列中的每个吸引子是否具有全局吸引性。

Cell-to-Cell Mapping Method was used to study the periodic orbits and period-doubling bifurcations of a moored ocean production platform subjected to waves. The mathematic model was a nonlinear oscillator driven by wave exciting force while the restoring force was exponential. The investigation on period-doubling bifurcations was presented by defining the period of wave exciting force as a bifurcation control paramet5er. Cell-to-Cell mapping method was used to find periodic orbits of the system and domains of attraction of different attractors. For every attractor, time history, phase plane portrait, power spectrum and Poincaré section were presented and then used to identify its type. It is shown that when the wave period is shorter than the critical one, there are competing attractors in this system which domains of attraction are twining each other. There are different period-doubling bifurcation characteristics in this system when the bifurcation parameter is in the different area of parameter space. Onset and abrupt disappearnce of a period-doubling bifurcation sequence are presented, while a bifurcation sequence converging to a chaotic attractor is also observed, where each attractor is global attracting. This phenomenon is clarified by using the results of Cell-to-Cell Mapping analysis.